Hi Januk,
a non-linear function will map lines to curves. Therefore, you e.g. may
replace every line by many lines, approximating the curve. E.g.:
graphics /. Line[{{x01_,y01_},{x02_,y02_}}]:>(calculate
x1..n,y1..n;Line[{{x1,y1},..,{xn,yn}}]
If you have more complicated graphics you must also deal with the case:
Line[{pt1,pt2,..ptn}].
Finally you could extend this scheme to geometric shapes like Circle e.t.c
hope this helps, Daniel
Januk wrote:
> Is there a way to have mathematica display a graphic using a non-
> linear scaling function? I want to scale any point on a 2D graphic by
> some non-linear function of the distance away from the origin. For a
> list of points, it is trivial to force the issue:
>
> pl3 = Graphics[{Point[
> RandomReal[{-20, 20}, {1000, 2}]
> ]
> }, Frame -> True, PlotRange -> All];
> GraphicsRow@{pl3,
> pl3 /. (xy : {x_?NumericQ, y_?NumericQ} :>
> Module[{r, \[Theta]},
> r = If[Norm[xy] == 0., 0, Log[1+Norm[xy]]];
> \[Theta] = If[Norm[xy] == 0., 0, ArcTan @@ xy];
> r {Cos[\[Theta]], Sin[\[Theta]]}
> ]
> )}
>
> Is there a way to do this for more complecated graphics (e.g. graphics
> with primitives)? For example:
>
> pl2 = Graphics[{
> Red, Point[RandomReal[{-2,2},{100,2}]],
> Orange, Line[{{-2, .75}, {2, .75}}],
> Green, Thick , Circle[{0, 0}, 2],
> Black, Point[{0, 0}]
> }]
>
> So far the technique of using a ReplaceAll simply transforms the end
> points of the line, not the line shape.
>
> Any thoughts of how to do this for an arbitrary Cartesian 2D graphic
> would be much appreciated.
>
> Thanks,
> Januk
>